Binghamton University Math Graduate Student Seminar

Spring 2020

Usual meetings: Thursdays at 4pm in WH 309

The Mathematics Graduate Student Seminar seeks to strengthen communication among grad students at Binghamton University, thereby cultivating our community and fostering a friendly environment in which to do mathematics research. We provide a venue for grad student talks on interesting math; we also hope to stimulate discussion around various topics--mathematical and otherwise--relevant to math grad students.

Presentations should be accessible to mathematics grad students, and all are encouraged to contribute a talk!

Email Matt Evans or Andrew Lamoureux (math emails evans and lamoureux resp) to schedule your talk!

For a list of talks from previous semesters, see the archives (link in the top left corner).

Schedule of Talks

23 January

Organizational Meeting

30 January

BUGCAT General Interest Meeting

This fall, we will have our 13th annual Binghamton University Graduate

Conference in Algebra and Topology (BUGCAT). This conference is largely run

by us graduate students, and helping organize the conference is a great

experience (that also looks good on CVs). At this meeting, I'll be talking

more about the conference and what's involved in making it happen. If you

are interested in BUGCAT but can't come, please feel free to email me

(alamour1@binghamton.edu).

6 February

NO SEMINAR

We encourage you to attend Selim Sukhtaiev's colloquium talk

on Anderson localization for disordered quantum graphs.

4:15-5:15pm in WH 100E

13 February

Garrett Proffitt

Introduction to infinite-type surfaces

We begin with an example from dynamics where the mapping class group of

infinite-surfaces arises naturally. Next we'll outline the proof of how

they are classified, and finally we'll look at examples of how results from

finite-type surfaces have been extended to infinite-type ones.

20 February

Matt Evans

Some recent results for spectra of commutative BCK-algebras

BCK-algebras are the algebraic semantics of a non-classical logic. Like for commutative rings,

there is a notion of a prime ideal in these algebras, and the set of prime ideals is a topological

space called the spectrum. By work of Stone (and later, Priestley), there is a close connection

between these spectra and distributive lattices with 0.

In this talk I will discuss some recent results on the interplay between commutative BCK-algebras,

their spectra, and distributive lattices.

27 February

No speaker

5 March

NO SEMINAR: Winter Break

12 March

Uly Alvarez

Upsetting the Grassmannian and some consequences

The Grassmannian for k dimensional linear subsets of R^n is G_k(R^n). Let P denote the coproduct of G_k(R^n),

where 0<k<n, considered as a topological poset partially ordered by inclusion.

With the usual topology, P has (n−1) connected components.

The order complex, Δ(P), is the subset of the join of G_k(R^n) as k goes from 1 to n−1, where

z = ∑_{k=1}^{n−1} t_k z_k is in Δ(P) if and only if i < j in supp(z) implies z_i < z_j.

Theorem: Using the up topology on P, there is a canonical weak homotopy equivalence f:Δ(P)→P.

The theorem holds for more general posets (given the right hypotheses) and generalizes an old theorem of McCord

for discrete posets. The hope for this talk is to sketch the proof for the case when n=2.

17 March (12-1pm, WH 329)

Wei Yang

Algebraic Probability

In mathematics, the idea of a free object is one of the basic concepts of abstract algebra. It is a

part of universal algebra, in the sense that it relates to all types of algebraic structure. In

addition to the well-known free object like free groups, tensor algebras, or free lattices. There

is some thing called “Free” Probability. Which is a relatively new area of research, that

connects linear algebra and probability.

26 March

Andrew Lamoureux

p-adic Numbers, Affine Schemes, and Differential Algebra

Here are the notes for Andrew's talk

2 April

Chris Eppolito

9 April

NO SEMINAR: Spring Break

16 April

Garrett Proffitt

21 April (12-1pm, WH 329)

28 April (12-1pm, WH 329)

5 May

Meenakshy Jyothis